The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested and investigated by Kress and Rundell for the electrostatic case and by Ivanyshyn and Kress for the time-harmonic case when the scattering object is a perfect conductor. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples.
© 2012 by Walter de Gruyter Berlin Boston